A017448 a(n) = (11*n + 4)^12.

16777216, 129746337890625, 95428956661682176, 6582952005840035281, 149587343098087735296, 1779197418239532716881, 13841287201000000000000, 79766443076872509863361, 367666387654882241806336, 1425760886846178945447841

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Crossrefs

Powers of the form (11*n+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), this sequence (m=12).

Programs

GAP

List([0..20], n-> (11*n+4)^12); # G. C. Greubel, Sep 18 2019

Magma

[(11*n+4)^12: n in [0..25]]; // Vincenzo Librandi, Apr 19 2011

Maple

seq((11*n+4)^12, n=0..20); # G. C. Greubel, Sep 18 2019

Mathematica

(11Range[0,20]+4)^12  (* Harvey P. Dale, Apr 18 2011 *)

PARI

vector(20, n, (11*n-7)^12) \\ G. C. Greubel, Sep 18 2019

Sage

[(11*n+4)^12 for n in (0..20)] # G. C. Greubel, Sep 18 2019

Formula

From G. C. Greubel, Sep 18 2019: (Start)

G.f.: (16777216 [phone]*x +93742255577726899*x^2 +5352495778795351967*x^3 +71415318201137477061*x^4 +320832301424673327498*x^5 +564873972371695167390*x^6 +409344222142040360670*x^7 +118792245587080463178*x^8 +12267852707472004709*x^9 +338777054867330431*x^10 +1156651444692563*x^11 [phone]*x^12)/(1-x)^13.

E.g.f.: (16777216 [phone]*x +47584732001339071*x^2 +1049509062475313902*x^3 +5159482909556787581*x^4 +9134471516437918728*x^5 +7332895074707269012*x^6 +3022504298573111220*x^7 +683555776881033507*x^8 +86991917430662915*x^9 +6131633113101001*x^10 [phone]*x^11 [phone]*x^12)*exp(x). (End)

a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13). - Wesley Ivan Hurt, Mar 18 2023